The manager of The Cheesecake Factory in Boston reports that on six randomly selected weekdays, the number of customers served was 175, 125,

Question

The manager of The Cheesecake Factory in Boston reports that on six randomly selected weekdays, the number of customers served was 175, 125, 180, 220, 240, and 245. She believes that the number of customers served on weekdays follows a normal distribution. Construct the 99% confidence interval for the average number of customers served on weekdays.

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Tài Đức 3 years 2021-09-03T07:16:31+00:00 1 Answers 23 views 0

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    2021-09-03T07:17:50+00:00

    Answer:

    (121.576 ; 273.424)

    Step-by-step explanation:

    Given the data:

    175, 125, 180, 220, 240, 245

    We can calculate the mean and standard deviation

    Mean = Σx/ n = 1185 / 6 = 197.5

    Standard deviation = 46.125 (calculator)

    The confidence interval :

    Mean ± margin of error

    Margin of Error = Tcritical * s/sqrt(n)

    Tcritical at 99%, df = n – 1 ; 6 – 1 = 5

    Tcritical = 4.032

    Margin of Error = 4.032 * 46.125/√6

    Margin of error = 75.924

    Confidence interval :

    197.5 ± 75.924

    Lower boundary = 197.5 – 75.924 = 121.576

    Upper boundary = 197.5 + 75.924 = 273.424

    (121.576 ; 273.424)

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